On the set covering polytope: I. all the facets with coefficients in {0, 1, 2}
Mathematical Programming: Series A and B
On the facial structure of the set covering polytope dimensional linear programming
Mathematical Programming: Series A and B
The fractional chromatic number of Mycielski's graphs
Journal of Graph Theory
Mathematical Programming: Series A and B
New Results on the Queens_n2 Graph Coloring Problem
Journal of Heuristics
A polyhedral approach to edge coloring
Operations Research Letters
Note: Facet-inducing web and antiweb inequalities for the graph coloring polytope
Discrete Applied Mathematics
A new DSATUR-based algorithm for exact vertex coloring
Computers and Operations Research
An exact approach for the Vertex Coloring Problem
Discrete Optimization
On optimal k-fold colorings of webs and antiwebs
Discrete Applied Mathematics
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We consider two (0, 1)-linear programming formulations of the graph (vertex-) coloring problem, in which variables are associated with stable sets of the input graph. The first one is a set covering formulation, where the set of vertices has to be covered by a minimum number of stable sets. The second is a set packing formulation, in which constraints express that two stable sets cannot have a common vertex, and large stable sets are preferred in the objective function. We identify facets with small coefficients for the polytopes associated with both formulations. We show by computational experiments that both formulations are about equally efficient when used in a branch-and-price algorithm. Next we propose some preprocessing, and show that it can substantially speed up the algorithm, if it is applied at each node of the enumeration tree. Finally we describe a cutting plane procedure for the set covering formulation, which often reduces the size of the enumeration tree.